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A plano-convex lens is made of glass of refractive index 1.5; its…
Question
A plano-convex lens is made of glass of refractive index 1.5; its convex face has radius of curvature 20 cm and its flat face is silvered, turning the device into an equivalent mirror. Treating the system as a thin combination (light refracts through the lens, reflects at the silvered flat face, and refracts back through the lens), find the magnitude of the focal length (in cm) of this equivalent mirror.
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Step-by-step solution
Lens focal length: 1/f = (n-1)(1/R1 - 1/R2) = 0.5*(1/20) = 1/40, so f = 40 cm, power P_L = 1/40 D(cm).
The flat silvered face is a plane mirror, power P_m = 0.
Equivalent mirror power P = 2P_L + P_m = 2/40 = 1/20.
Equivalent focal length = 1/P = 20 cm.
Final answer20
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